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How do you simplify #(3t)/( 2-x) + 5/(x-2)#?

Answer 1

Kennedy Adams

#(3t-5)/(2-x)#

#5/(x-2) = (-5)/(2-x)#

Therefore #color(white)("XXX")(3t)/(2-x) +5/(x-2)#

#color(white)("XXX")=(3t)/(2-x) + (-5)/(2-x)#

#color(white)("XXX")=(3t-5)/(2-x)#

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Answer 2

Eva Adamson

To simplify the expression (3t)/(2-x) + 5/(x-2), we need to find a common denominator and combine the fractions. The common denominator is (2-x)(x-2).

Multiplying the first fraction by (x-2)/(x-2) and the second fraction by (2-x)/(2-x), we get:

[(3t)(x-2)]/[(2-x)(x-2)] + [5(2-x)]/[(2-x)(x-2)]

Expanding and combining the numerators, we have:

(3tx - 6t + 10 - 5x)/[(2-x)(x-2)]

Simplifying the numerator, we get:

(3tx - 5x - 6t + 10)/[(2-x)(x-2)]

Therefore, the simplified expression is (3tx - 5x - 6t + 10)/[(2-x)(x-2)].

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.